It's possible that there may be a connection, but I can't say positively.
I am presently focused on a Hezekiah Davenport that was born 22 or 23 October 1767, possibly in Little Compton, Rhode Island. This individual married a Nelly Babcock (B. 5 Jul 1803, d. 27 October 1848) Hezekiah had at least one child named Benjamin (gg), and possibly another son named Charles N. This Hezekiah and Nelly are buried in Robertson Cemetery, Tompkins County, New York. They reportedly lived in the Ithaca, Dryden, Homer area of Tompkins County. Records for this cemetery also indicate births/deaths of two additional sons for Hezekiah and Nelly, however, One was born 2 yrs 8 mos after Hezekiah's death and the second, died at 1 yr 3 mos old in 1848. I'm proceeding cautiously. If anything in here meshes with any additional data you may have or come across, I would be happy to hear from you. Thank you for your reply.